Basically you gain superiority by capturing and holding key areas. To capture an area, kill non-friendly aircraft over it or groups ground targets within. Friendly aircraft deaths over an area moves back the capture of said area (for example, killing a hostile Zero gets you +40 points to capture the area, dying as a Zero gets you -40 points). Each area gives +3 superiority per second and some other bonuses. After a while, the Squall line comes up and stops all respawning (if you're dead before the Squall line hits, you can still respawn. If you die after it hits, you're gone for good).

The match is over once either team reaches the superiority limit or one of the teams runs out of aircraft after the Squall line. That's pretty much all the basics aside of "shoot plane, plane go boom "